We report on sealed-bid second-price auctions that we conducted on the Internet using subjects with substantial prior experience: they were highly experienced participants in eBay auctions. Unlike the novice bidders in previous (laboratory) experiments, the experienced bidders exhibited no greater tendency to overbid than to underbid. However, even subjects with substantial prior experience tended not to bid their values, suggesting that the non-optimal bidding of novice subjects is robust to substantial experience in non-experimental auctions. We found that auction revenue was not significantly different from the expected revenue the auction would generate if bidders bid their values. Auction efficiency, as measured by the percentage of surplus captured, was substantially lower in our SPAs than in previous laboratory experiments. 2011 Economic Science Association.

If bidders have independent private values and homogeneous entry costs, a first- or second-price auction with a reserve price equal to the seller's value maximizes social surplus and seller revenue. We show that if entry costs are heterogeneous and private information, then the revenue-maximizing reserve price is above the seller's value, a positive admission fee (and a reserve price equal to the seller's value) generates more revenue, and an entry cap combined with an admission fee generates even more revenue. Social surplus and seller revenue may either increase or decrease in the number of bidders, but they coincide asymptotically. 2011, RAND.

We study two-person extensive form games, or "matches," in which the only possible outcomes (if the game terminates) are that one player or the other is declared the winner. The winner of the match is determined by the winning of points, in "point games." We call these matches binary Markov games. We show that if a simple monotonicity condition is satisfied, then (a) it is a Nash equilibrium of the match for the players, at each point, to play a Nash equilibrium of the point game; (b) it is a minimax behavior strategy in the match for a player to play minimax in each point game; and (c) when the point games all have unique Nash equilibria, the only Nash equilibrium of the binary Markov game consists of minimax play at each point. An application to tennis is provided. 2010 Elsevier Inc.

eBay's Buy It Now format allows a seller to list an auction with a "buy price" at which a bidder may purchase the item immediately and end the auction. When bidders are risk averse, then theoretically a buy price can raise seller revenue when values are private (but not when values are common). We report the results of laboratory experiments designed to determine whether in practice a buy price is advantageous to the seller. We find that a suitably chosen buy price yields a substantial increase in seller revenue when values are private, and a small (but statistically insignificant) increase in revenue when values are common. In both cases a buy price reduces the variance of seller revenue. A behavioral model which incorporates the winner's curse and the overweighting by bidders of their own signal explains the common value auction data better than the rational model. 2010 Elsevier Inc.

Experiments on second-price sealed-bid private value auctions have established that subjects typically bid more than their value, despite the fact that value bidding is a dominant strategy in such auctions. Moreover, the laboratory evidence shows that subjects do not learn to bid their values as they gain more experience. In the present paper, we re-examine the second-price auction data from Kagel and Levin's (Econ J 103:868-879, 1993) classic paper. We find that auction efficiency increases over time, even though the frequency of overbidding is unchanged. We argue that the rise in efficiency is due to a decline in the variability of overbidding. This is consistent with subjects' learning to bid more like each other. 2010 The Author(s).

Does expertise in strategic behavior obtained in the field transfer to the abstract setting of the laboratory? Palacios-Huerta and Volij (2008) argued that the behavior of professional soccer players in mixed-strategy games conforms closely to minimax play, while the behavior of students (who are presumably novices in strategic situations requiring unpredictability) does not. We reexamine their data, showing that the play of professionals is inconsistent with the minimax hypothesis in several respects: (i) professionals follow nonstationary mixtures, with action frequencies that are negatively correlated between the first and the second half of the experiment, (ii) professionals tend to switch between under- and overplaying an action relative to its equilibrium frequency, and (iii) the distribution of action frequencies across professionals is far from the distribution implied by minimax. In each respect, the behavior of students conforms more closely to the minimax hypothesis. 2010 The Econometric Society.

In markets with adverse selection, only low-quality units trade in the competitive equilibrium when the average quality of the good held by sellers is low. We show that under decentralized trade, however, both high- and low-quality units trade, although with delay. Moreover, when frictions are small, the surplus realized is greater than the (static) competitive surplus. Thus, decentralized trade mitigates the lemons problem. Remarkably, payoffs are competitive as frictions vanish, even though both high- and low-quality units continue to trade, and there is trade at several prices. (2010) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

eBay and Yahoo allow sellers to list their auctions with a buy price at which a bidder may purchase the item immediately. On eBay, the buy-now option disappears once a bid is placed, while on Yahoo the buy-now option remains in effect throughout the auction. We show that when bidders are risk averse, both types of auctions raise seller revenue for a wide range of buy prices. The Yahoo format raises more revenue than the eBay format when bidders have either CARA or DARA. Bidders with DARA prefer the eBay auction, while bidders with CARA are indifferent between the two. 2006 Springer-Verlag.

Employing a procedure suggested by a simple theoretical model of auctions in which bidders and sellers have observable and heterogenous reputations for default, we examine the effect of reputation on price in a data set drawn from the online auction site eBay. Our main empirical result is that seller's, but not bidder's, reputation has an economically and statistically significant effect on price. 2006 Blackwell Publishing.

Sales of multiple real-estate properties are often conducted via a sequence of ascending auctions, giving the winner at each stage the right to choose one of the available lots. We show that when bidders are risk averse, such bidders' choice auctions raise more revenues than standard simultaneous or sequential ascending auctions. We also report the results of laboratory experiments to investigate the effectiveness of bidders' choice auctions vis-a-vis the simultaneous ascending auction. The revenue-superiority of the bidders' choice auction is corroborated by the experimental data. Finally, we compare observed bidding behavior in the experiments with theoretically predicted bids to estimate a common risk aversion parameter from the data. 2004 by the European Economic Association.

This paper deals with a general version of a two-stage model of R&D and product market competition. We provide a thorough generalization of previous results on the comparative performance of noncooperative and cooperative R&D, dispensing in particular with ex-post firm symmetry and linear demand assumptions. We also characterize the structure of profit-maximizing R&D cartels where firms competing in a product market jointly decide R&D expenditure, as well as internal spillover, levels. We establish the firms would essentially always prefer extremal spillovers, and within the context of a standard specification, derive conditions for the optimality of minimal spillover. 2003 Elsevier Science (USA). All rights reserved.

We characterize the dynamics of trading patterns and market composition when trade is bilateral, finding a trading partner is costly, prices are determined by bargaining, and preferences are private information. We show that equilibrium is inefficient and exhibits delay as sellers price discriminate between buyers with different values. As frictions vanish, transaction prices are asymptotically competitive and the welfare loss of inefficient trading approaches zero, even though the trading patterns continue to be inefficient and delay persists. Journal of Economic Literature Classification Numbers: D40, D50. 2002 Elsevier Science (USA).

We study equilibrium and maximin play in supergames consisting of the sequential play of a finite collection of stage games, where each stage game has two outcomes for each player. We show that for two-player supergames in which each stage game is strictly competitive, in any Nash equilibrium of the supergame, play at each stage is a Nash equilibrium of the stage game provided preferences over certain supergame outcomes satisfy a natural monotonicity condition. In particular, equilibrium play does not depend on risk attitudes. We establish an invariance result for games with more than two players when the solution concept is subgame perfection. Journal of Economic Literature Classification Numbers: C72, C9. 2001 Academic Press.

We characterize the dynamics of trading patterns and market composition when trade is bilateral, finding a trading partner is costly, prices are determined by bargaining, and preferences are private information. We show that equilibrium is inefficient and exhibits delay as sellers price discriminate between buyers with different values. As frictions vanish, transaction prices are asymptotically competitive and the welfare loss of inefficient trading approaches zero, even though the trading patterns continue to be inefficient and delay persists.

We consider a two-period duopoly characterized by a one-way spillover structure in process R&D and a very broad specification of product market competition. We show that a priori identical firms always engage in different levels of R&D, at equilibrium, thus giving rise to an innovator/imitator configuration and ending up with different sizes. We also provide a general analysis of the social benefits of, and firms' incentive for, forming research joint ventures. Another contribution is methodological, illustrating how submodularity (R&D decisions are strategic substitutes) can be exploited to provide a general analysis of a R&D game. Journal of Economic Literature Classification Numbers: C72, L13, O31. 2000 Academic Press.

We analyze trading in a model in which the agents and their preferences are the same as in the main models of matching and bargaining, but in which trade is centralized rather than decentralized. We characterize equilibrium when trade is centralized and, by comparing our results with results from the matching literature, we show conditions under which decentralized trading processes reproduce the allocations of our centralized one. We establish that the competitive price as defined in the matching literature (i.e., relative to the stocks, flows, or totals) coincides, in the appropriate setting, with the equilibrium price in our model.

We consider a model in which firms first choose process R&D expenditures and then compete in an output market. We show the symmetric equilibrium under R&D competition is sometimes unstable, in which case two asymmetric equilibria must also exist. For the latter, we find, in contrast to the literature that total profits are sometimes higher with R&D competition than with research joint venture cartelization (due to the cost asymmetry of the resulting duopoly in the noncooperative case). Furthermore, these equilibria provide another instance of R&D-induced firm heterogeneity.

We show that the equilibrium of a matching and bargaining model of a market in which there is a finite number of agents at each date need not be near the equilibrium of a market with a continuum of agents, although matching probabilities are the same in both markets. Holding the matching process fixed, as the finite market becomes large its equilibrium approaches the equilibrium of its continuum limit.

This paper reports the results of an experiment designed to test the usefulness of alternative solution concepts to explain players' behavior in noncooperative games with preplay communication. In the experiment subjects communicate by plain conversation prior to playing a simple game. In this setting, we find that the presumption of individualistic and independent behavior underlying the concept of Nash equilibrium is inappropriate. Instead, we observe behavior to be coordinated and correlated. Statistical tests reject Nash equilibrium as an explanation of observed play. The coalition proof correlated equilibrium of the game, however, explains the data when the possibility of errors by players is introduced. Journal of Economic Literature Classification Numbers: C72, C92. 1998 Academic Press.

We show that a profit maximizing monopolistic intermediary may behave approximately like a Walrasian auctioneer by setting bid and ask prices nearly equal to Walrasian equilibrium prices. In our model agents choose to trade either through the intermediary or privately. Buyers (sellers) trading through the intermediary potentially trade immediately at the ask (bid) price, but sacrifice the spread as gains. A buyer or seller who trades privately shares all the gains to trade with this trading partner, but risks costly delay in finding a partner. We show that as the cost of delay vanishes, the equilibrium bid and ask prices converge to the Walrasian equilibrium prices. Springer-Verlag 1997.

We characterize the agreements that the players of a noncooperative game may reach when they can communicate prior to play, but they cannot reach binding agreements: A coalition-proof equilibrium is a correlated strategy from which no coalition has an improving and self-enforcing deviation. We show that any correlated strategy whose support is contained in the set of actions that survive the iterated elimination of strictly dominated strategies and weakly Pareto dominates every other correlated strategy whose support is contained in that set, is a coalition-proof equilibrium. Consequently, the unique equilibrium of a dominance solvable game is coalition-proof. Journal of Economic Literature Classification Numbers: C72, D82. 1996 Academic Press, Inc.

Other

Even though adverse selection pervades markets for real goods and financial assets, equilibrium in such markets is not well understood. What are the properties of equilibrium in dynamic markets for lemons? What determines the
liquidity of a good? Which market structures perform better, decentralized ones, in which trade is bilateral and prices are negotiated, or centralized ones, in which trade is multilateral and agents are price-takers? Is there a role
for government intervention? We show that when the horizon is finite and frictions are small, decentralized markets are more liquid and perform better than centralized markets. Moreover, the surplus realized is above the static
competitive surplus, and decreases as the horizon grows larger, approaching the static competitive surplus as the horizon becomes infinite even if frictions are non-negligible. Subsidies on low quality or taxes on high quality raise
surplus.

We explore the role of experience in mixed-strategy games by comparing, for a stylized version of Texas Hold-em, the behavior of experts, who have extensive experience playing poker online, to the behavior of novices. We find
significant differences. The initial frequencies with which players bet and call are closer to equilibrium for experts than novices. And, while the betting and calling frequencies of both types of subjects exhibit too much heterogeneity
to be consistent with equilibrium play, the frequencies of experts exhibit less heterogeneity. We find evidence that the style of online play transfers from the field to the lab.

We consider a two-period duopoly characterized by a one-way spillover structure in process R&D and a very broad specification of product market competition. We show that a priori identical firms always engage in different levels of R&D, at equilibrium, thus giving rise to an innovator/imitator configuration and ending up with different sizes. We also provide a general analysis of the social benefits of, and firms incentive for, forming research joint ventures. The key properties of the game are submodularity (R&D decisions are strategic substitutes) and lack of global concavity.

We consider a two-period duopoly characterized by a one-way
spillover structure in process R&D and a very broad
specification of product market competition. We show that a
priori identical firms always engage in different levels of
R&D, at equilibrium, thus giving rise to an
innovator/imitator configuration and ending up with
different sizes. In view of this endogenous firm
heterogeneity, the social benefits of, and the firms'
incentives for, research joint ventures are somewhat
different from the case of ex post firm symmetry. The key
properties of the game are submodularity (R&D decisions are
strategic substitutes) and lack of global concavity.

We study the impact of public and secret reserve prices in auctions where buyers have independent private values and heterogeneous entry costs. We find that in a standard auction the optimal (i.e., revenue maximizing) public reserve price is typically above the seller's value. Moreover, an appropriate entry fee together with a public reserve price equal to the seller's value generates greater revenue. Secret reserve prices, however, differ across auction formats. In a second-price sealed-bid auction the secret reserve price is above the optimal public reserve price; hence there is less entry, a smaller probability of sale, and both the seller revenue and the bidders' utility are less than with an optimal public reserve price. In contrast, in a first-price sealed-bid auction the secret reserve is equal to the seller's value, and the bidders' expected utility (seller revenue) is greater (less) than with an optimal public reserve price.

With one-way spillovers, the standard symmetric two-period R&D model leads to an asymmetric equilibrium only, with endogenous innovator and imitator. We show how R&D decisions and measures of firm heterogeneity - market shares, R&D shares, and profits - depend on spillovers and on R&D costs. While a joint lab always improves on consumer welfare, it yields higher profits, cost reductions and social welfare only under extra assumptions, beyond those required with multi-directional spillovers. Finally, the novel issue of optimal R&D cartels (with an endogenous spillover parameter) is addressed. In particular, the latter can be zero under some conditions.

This paper reports the results of an experiment designed to test the usefulness of alternative solution concepts to explain players' behavior in noncooperative games with preplay communication. In the experiment subjects communicate byplain conversationprior to playing a simple game. In this setting, we find that the presumption ofindividualisticandindependentbehavior underlying the concept of Nash equilibrium is inappropriate. Instead, we observe behavior to becoordinatedandcorrelated. Statistical tests reject Nash equilibrium as an explanation of observed play. The coalition proof correlated equilibrium of the game, however, explains the data when the possibility of errors by players is introduced

This paper reports the results of an experiment designed to test the usefulness of alternative solution concepts to explain players' behavior in noncooperative games with preplay communication. In the experiment subjects communicate by plain conversation prior to playing a simple game. In this setting, we find that the presumption of individualistic and independent behavior underlying the concept of Nash equilibrium is inappropriate. Instead, we observe behavior to be cooperative and correlated. Statistical tests reject Nash equilibrium as an explanation of observed play. The coalition proof equilibrium of the game, however, explains the data when the possibility of errors by players is introduced.